An Analytic Potential Model for Symmetric and Asymmetric DG MOSFETs

Manuscript received July 18, 2005; revised November 14, 2005. This work was supported by SRC Project 2003-NJ-1131.1001. The review of this paper was arranged by Editor T. Skotnicki. The authors are with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093 USA (e-mail: hlu@; taur@). Digital Object Identifier 10.1109/TED.2006.872093
Abstract—This paper presents an analytic potential model for long-channel symmetric and asymmetric double-gate (DG) MOSFETs. The model is derived rigorously from the exact solution to Poisson’s and current continuity equation without the charge-sheet approximation. By preserving the proper physics, volume inversion in the subthreshold region is well accounted for in the model. The resulting analytic expressions of the drain–current, terminal charges, and capacitances for longchannel DG MOSFETs are continuous in all operation regions, i.e., linear, saturation, and subthreshold, making it suitable for compact modeling. As no fitting parameters are invoked throughout the derivation, the model is physical and predictive. All parameter formulas are validated by two-dimensional numerical simulations with excellent agreement. The model has been implemented in Simulation Program with Integrated Circuit Emphasis version 3 (SPICE3), and the feasibility is demonstrated by the transient analysis of sample CMOS circuits. Index Terms—Analytic potential model, compact model, double-gate (DG) MOSFET.
and above threshold regions [5], which will potentially cause convergence problems. Another model, although continuous and analytic, is based on the approximate solution to onedimensional (1-D) Poisson’s and current continuity equations and requires some fitting parameters [6]. In this paper, we rigorously solve Poisson’s equation to obtain analytic potential expression and, further, derive the implicit drain–current model based on current continuity equation. We then proceed to develop charge and capacitance models. This methodology is applied to the derivation of both symmetric DG (SDG) and asymmetric DG (ADG) MOSFETs. As the model involves implicit functions, iterations are required to solve the equations. It is shown that the results of the analytic model exhibit excellent agreement with two-dimensional (2-D) numerical simulation values, and yet, the expressions are continuous in all operation regions. Sections II and III are devoted to the development of SDG and ADG MOSFETs, respectively. Finally, the implementation in SPICE3 is discussed, and the transient analysis of sample circuit is demonstrated in Section IV.
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 5, MAY 2006
1161
An Analytic Potential Model for Symmetric and Asymmetric DG MOSFETs
Huaxin Lu, Student Member, IEEE, and Yuan Taur, Fellow, IEEE

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II. ANALYTIC POTENTIAL MODEL FOR SDG MOSFETs A. Current and Transconductance Model for SDG MOSFETs In our previous paper [7], we proposed an analytic drain–current model for SDG MOSFETs. The model continuously covers all operation regions and is in excellent agreement with 2-D numerical simulation results without any ad hoc fitting parameters. These features enable the model to be an ideal kernel of SDG MOSFET modeling. In this section, we first briefly review the drain–current model. Then, starting from the drain–current expression, we further carry on the derivation to develop the intrinsic charge and capacitance models of SDG MOSFETs, which are required to perform transient analysis in circuit simulation. Consider an undoped (or lightly doped) SDG MOSFET shown schematically in Fig. 1. Poisson’s equation along a vertical cut perpendicular to the Si film (Fig. 2) takes the following form with only the mobile charge (electrons) term:
I. INTRODUCTION OMPACT models of MOSFETs have evolved from piecewise models to unified models due to the numerical divergence problems in circuit simulation caused by discontinuous derivatives of MOSFET models [1], [2]. For bulk MOSFETs, Pao-Sah’s double integral based on gradual-channel approximation (GCA), although valid in all operation regions, cannot be carried out analytically due to the presence of both depletion and mobile charges in the integral [3]. This necessitates the charge-sheet approximation that would lead to further simplification to obtain a piecewise explicit current expression. However, charge-sheet-based models cannot properly describe volume inversion, a unique characteristic of double-gate (DG) MOSFETs in the subthreshold region [4]. Contrary to bulk MOSFETs, depletion charges in DG MOSFETs are negligible because the silicon film is undoped (or lightly doped). Thus, only the mobile charge term needs to be included in Poisson’s equation. Therefore, the exact solutions to Poisson’s and current continuity equations based on GCA can be derived without the charge-sheet approximation. Several drain–current models for DG MOSFETs have been proposed previously. One model that allows two gates independently driven adopts a smooth function to join the subthreshold